Import Question JSON

Current Question (ID: 8933)

Question:

$\text{A person standing on the floor of an elevator drops a coin. The coin reaches the floor in time } t_1\text{, if the elevator is moving uniformly and time } t_2\text{, if the elevator is stationary. Then:}$

Options:

1. $t_1 < t_2 \text{ or } t_1 > t_2 \text{ depending upon whether the lift is going up or down.}$
2. $t_1 < t_2$
3. $t_1 > t_2$
4. $t_1 = t_2$

Solution:

$\text{Hint: } s = ut + \frac{1}{2}at^2$ $\text{Step: Find the relation between both time.}$ $\text{From the elevator frame, the initial velocity of the coin w.r.t. floor is zero.}$ $\text{The time taken by the coin to reach the ground is given by:}$ $t = \sqrt{\frac{2h}{g_{eff}}} \text{ [h = height of the release point of coin and floor]}$ $\text{In both the cases, either elevator is moving uniformly or stationary, } g_{eff} = g\text{.}$ $\text{Therefore, time taken by the coin to reach the ground will same in both cases i.e., } t_1 = t_2$ $\text{Hence, option (4) is the correct answer.}$

Import JSON File

Upload a JSON file containing LaTeX/MathJax formatted question, options, and solution.

Expected JSON Format:

{
  "question": "The mass of carbon present in 0.5 mole of $\\mathrm{K}_4[\\mathrm{Fe(CN)}_6]$ is:",
  "options": [
    {
      "id": 1,
      "text": "1.8 g"
    },
    {
      "id": 2,
      "text": "18 g"
    },
    {
      "id": 3,
      "text": "3.6 g"
    },
    {
      "id": 4,
      "text": "36 g"
    }
  ],
  "solution": "\\begin{align}\n&\\text{Hint: Mole concept}\\\\\n&1 \\text{ mole of } \\mathrm{K}_4[\\mathrm{Fe(CN)}_6] = 6 \\text{ moles of carbon atom}\\\\\n&0.5 \\text{ mole of } \\mathrm{K}_4[\\mathrm{Fe(CN)}_6] = 6 \\times 0.5 \\text{ mol} = 3 \\text{ mol}\\\\\n&1 \\text{ mol of carbon} = 12 \\text{ g}\\\\\n&3 \\text{ mol carbon} = 12 \\times 3 = 36 \\text{ g}\\\\\n&\\text{Hence, 36 g mass of carbon present in 0.5 mole of } \\mathrm{K}_4[\\mathrm{Fe(CN)}_6].\n\\end{align}",
  "correct_answer": 4
}